# Recent questions tagged gateme-2019-set1

John Thomas, an _________ writer, passed away in $2018$. imminent prominent eminent dominant
____I permitted him to leave, I wouldn’t have had any problem with him being absent, ____ I? Had, wouldn’t Have, would Had, would Have, wouldn’t
A worker noticed that the hour hand on the factory clock had moved by $225$ degrees during her stay at the factory. For how long did she stay in the factory? $3.75$ hours $4$ hours and $15$ mins $8.5$ hours $7.5$ hours
The sum and product of two integers are $26$ and $165$ respectively. The difference between these two integers is ______ $2$ $3$ $4$ $6$
The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of ______ the issue. collaring skirting tying belting
Under a certain legal system, prisoners are allowed to make one statement. If their statements turns out to be true then they are hanged. If the statements turns to be false then they are shot. One prisoner made a statement and the judge had no option but to set ... of the following could be that statement? I did not commit the crime I committed the crime I will be shot You committed the crime
A person divided an amount of Rs. $100,000$ into two parts and invested in two different schemes. In one he got $10 \%$ profit and in the other he got $12 \%$. If the profit percentages are interchanged with these investments he would have got Rs. $120$ less. Find the ratio between his investments in the two schemes. $9:16$ $11:14$ $37:63$ $47:53$
Congo was named by Europeans, Congo's dictator Mobuto later changed the name of the county and the river to Zaire with the objective of Africanising names of persons and spaces. However, the name Zaire was a Portuguese alteration of Nzadi O Nzere, a local ... to Africanise names was prevented by the Portuguese As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire
A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skills levels of total employment in $2010$ is given in the pie chart as shown. There were a total of $600$ employees in $2010$ and the total employment increased by $15\%$ ... $40 \%$ from $2010$ to $2016$, how many employees were there at skill level T in $2016$? $30$ $35$ $60$ $72$
$M$ and $N$ had four children $P$, $Q$, $R$ and $S$. Of them, only $P$ and $R$ were married. They had children $X$ and $Y$ respectively. If $Y$ is a legitimate child of $W$, which of the following statements is necessarily FALSE? $M$ is the grandmother of $Y$ $R$ is the father of $Y$ $W$ is the wife of $R$ $W$ is the wife of $P$
1 vote
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around x-axis is $\dfrac{\pi}{4} \\$ $\dfrac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
For the equation $\dfrac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is $\dfrac{7}{3}e^{-7/3} \\$ $\dfrac{7}{3}e^{-3/7} \\$ $\dfrac{3}{7}e^{-7/3} \\$ $\dfrac{3}{7}e^{-3/7}$
The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the percentage of rods whose lengths lie between $438$ mm and $441$ mm? $81.85 \%$ $68.4 \%$ $99.75 \%$ $86.64 \%$
A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular velocity $\omega$. At time $t=0$, the vertical position of the follower is $y(0)=0$, and the system is in the configuration shown below: The vertical position of the follower face, $(y(t)$ is given by $e \sin \omega t$ $e(1+ \cos 2 \omega t)$ $e(1- \cos \omega t)$ $e \sin 2 \omega t$
The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $2 \\$ $4$
A spur gear with $20^{\circ}$ full depth teeth is transmitting $20 \: kW$ at $200 \: rad/s$. The pitch circle diameter of the gear is $100 \: mm$. The magnitude of the force applied on the gear in the radial direction is $0.36 \: kN$ $0.73 \: kN$ $1.39 \: kN$ $2.78 \: kN$
During a non-flow thermodynamic process $(1-2)$ executed by a perfect gas, the heat interaction is equal to the work interaction $(Q_{1-2} = W_{1-2})$ when the process is Isentropic Polytropic Isothermal Adiabatic
For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section, the Nusselt number at constant wall heat flux $(Nu_q)$ and that at constant wall temperature $(Nu_T)$ are related as $Nu_q > Nu_T$ $Nu_q < Nu_T$ $Nu_q = Nu_T$ $Nu_q = (Nu_T)^2$
As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are Kaplan, Francis, Pelton Pelton, Francis, Kaplan Francis, Kaplan, Pelton Pelton, Kaplan, Francis
A slender rod of length $L$, diameter $d$ $(L > >d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, to form a composite cylindrical rod of length $2L$. The heat transfer in radial direction and contact resistance are ... the composite rod is $k_1+k_2 \\$ $\sqrt{k_1k_2} \\$ $\dfrac{k_1k_2}{k_1+k_2} \\$ $\dfrac{2k_1k_2}{k_1+k_2}$
Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle? Coefficient of performance is ... of performance is the same as that of the original cycle Refrigerating effect is lower than that of the original cycle
In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is called blister sprue riser pin hole
Which one of the following welding methods provides the highest heat flux $(W/mm^2)$? Oxy-acetylene gas welding Tungsten inert gas welding Plasma arc welding Laser beam welding
The length, width and thickness of a steel sample are $400$ mm, $40$ mm and $20$ mm, respectively. Its thickness needs to be uniformly reduced by $2$ mm in a single pass by using horizontal slab milling. The milling cutter (diameter: $100$ mm, width: $50$ mm) has $20$ teeth and rotates at $1200$ rpm ... machining task are $14$ mm, $18.4$ s $21$ mm, $28.9$ s $21$ mm, $39.4$ s $14$ mm, $21.4$ s
The position vector $\overrightarrow{OP}$ of point $P(20,10)$ is rotated anti-clockwise in $X-Y$ plane by an angle $\theta = 30^{\circ}$ such that point $P$ occupies position $Q$, as shown in the figure. The coordinates $(x,y)$ of $Q$ are $(13.40,22.32)$ $(22.32, 8.26)$ $(12.32, 18.66)$ $(18.66, 12.32)$
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is ... $490$ $510$ $530$ $536.67$
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)
Water flows through a pipe with a velocity given by $\overrightarrow{V}= \bigg( \dfrac{4}{t}+x+y \bigg) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ direction, $t(>0)$ is in seconds, and $x$ and $y$ are in meters. The magnitude of total acceleration at the point $(x,y)=(1,1)$ at $t=2\: s$ is ______$m/s^2$
Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas constant of $0.287 \: kJ/kg.K$, the change in entropy of air (in $kJ/kg.K$, round off to two decimal places) is ______
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then strain ... same specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.
The set of equations $\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$ has infinite solutions, if $a=$ $-3$ $3$ $4$ $-4$
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy-2x^2+2y^2+ \text{constant}$ $4y^2-4xy + \text{constant}$ $2x^2-2y^2+ xy + \text{constant}$ $-4xy+2y^2-2x^2+ \text{constant}$
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between the front and rear wheels. The distance between front and rear wheel is $l$. The acceleration of the car is $a$, and acceleration ... $R_f=R_r = \dfrac{W}{2}+\dfrac{W}{g} \bigg( \dfrac{h}{l} \bigg) a$
In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm$ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of $10 \: rad/s$. The magnitude of angular velocity (in rad/s) of bar DC at this instant is $0$ $10$ $15$ $25$